teaching area and perimeter
I blogged a few days ago about some of the fun area and perimeter activities we had done in class (If you missed it, just CLICK HERE.) and I promised you a follow-up post!

With "big" concepts, I tend to have a sequence of teaching that doesn't really follow a formula but does have a certain sequence.  First of all, I want the students to explore and build their understanding.  That's what that first post was all about--immersing students in meaningful activities to develop their foundations.

Once that happens, we do need some guided practice and formative assessment to see where students are with their depth of understanding.  Sometimes this means I use some of the lessons that area a part of our math series, sometimes it involves other practice activities.  After I taught a few mini-lessons from our math series, I wanted to give students the opportunity to practice finding area and perimeter--and time for me to observe and look for any misconceptions and problems.

Here's what I did.  I used a set of task cards that were differentiated by level and put them in a giant circle around the room (I couldn't 'get a good picture that showed this!  Just picture 20 cards scattered around the perimeter!).  I explained to the students that the cards asked them to find area and perimeter--and were arranged in order from most simple--rectangles and shapes with the grid built in--to more complex shapes.  I partnered students up with partners of similar math abilities and asked them to start at a location that they thought matched their confidence level.

 I asked them to take a wipe off marker, their math spiral, and something to erase with (most of my students have a sock or washcloth in their desk).  Their job was to solve a card as a team, make sure they used math talk to "prove" that their solutions were correct.  I encouraged them to write directly on the cards to help with that "proof".  As they solved a card, they then moved to another one.
teaching area and perimeterteaching area and perimeter
 I had a blast walking around and listening to their thinking...this card was being tackled by some of my struggling students.  The strategy?  One of them suggested "moving" the bottom two squares over to the end to make it a rectangle which would be easier to count.  It took some convincing to get her partner to believe it (we actually broke out some tiles and built it) but the light bulb went ON after that!
area and perimeter lessons
 We had investigated two strategies for finding the area of these irregular shapes--finding the entire rectangle and subtracting the missing "bite", and subdividing the shape into smaller rectangles.  If students were working quickly, I asked them to try both methods to confirm if they were getting the same amount.
area and perimeter task cards
 This partnership was REALLY struggling with their math talk!  (See that really dark blue line?  She traced over it about 12 times to try to make her point!).  The two students had totally different answers and neither were having much success being open to other ideas.  I listened to them for a little while and then asked another partnership to join them to try to get them "unstuck".  It worked.
area and perimeter lessons
 I was able to keep a running list of students who seemed to be struggling--but the best part was that there was some amazing teaching being done from student to student!  The next day, I gave an entrance slip to take the temperature of the group, refined my "watch" list, and then planned for some reteaching for those who needed it.  Not bad for about 25 minutes of math class!
area and perimeter ideas

Interested in checking out these task cards?

How about some area and perimeter formative assessments?

Want to pin this post for later?

Today's my day to blog over at Upper Elementary Snapshots!  Just click the image above to take you to today's post...hope you enjoy it.
math homework
As I approach my fifth year of blogging (YIKES!), I cannot tell you how touched I have been by the connections I have made with teachers around the world. I have learned so much from them--and I hope I have been able to give a little in return.

One topic that ALWAYS gets people a little ramped up is...


That's right.  Just bring THAT topic up to a group of parents--or teachers--and see the mixed reviews you get!  You can find all sorts of studies that talk about the benefits (or not) of homework...but I caution you to always take note of the age group studied!  Most of the research out that was done with high school students!  Check out this statement from an article on Edutopia that tries to clarify this.

"Although the debate about homework generally falls in the "it works" vs. "it doesn't work" camps, research shows that grade level makes a difference. High school students generally get the biggest benefits from homework, with middle school students getting about half the benefits, and elementary school students getting little benefit (Cooper et al., 2006). Since young students are still developing study habits like concentration and self-regulation, assigning a lot of homework isn't all that helpful."

So, that being said, I DO give occasional homework. In fact, I do require my students to read a minimum of 20 minutes daily at least 5 times per week.  Why?  I am wanting them to build a reading habit!  There are no rules--it can be the same book they are reading at school, articles online, cartoons, magazines--anything that builds their "readerly life".

I also at times will assign homework something like this:  "Find someone not in our class to teach about the difference between potential and kinetic energy."  By keeping it this open-ended, it can be a parent.  A babysitter.  A sibling.  A friend.  Even ME if necessary.  This type of homework is fast and easy and is very reinforcing of what is being done at school.

Finally, I do assign a little math homework at times...but not what people might typically think.  I do not want parents having to teach math.  I'm a little possessive of that!  I don't want homework to be stressful for anyone--so any math homework I give is either fluency work (skills they are secure with and are just building automaticity) or open-ended in nature.  If I don't think a student can handle a task, I replace it with a fluency game.  Because I believe this strongly, I will often assign a practice page from a unit earlier in the year.  Of course, it's super important to communicate this to parents...that the homework doesn't match the topic OR level of classwork...and that it is meant to build responsibility and fluency not reinforce that day's lesson.

When I talk about open-ended homework, I am referring to work that is, by its very nature, differentiated.  Check out these pictures from some homework we did within the last week or so--and note that these would be FANTASTIC for classwork as well--but they are wonderful for homework because they are so flexible.  I love using these--we had done a multiplication review (it IS testing season) so I gave them one to do--and then space to make up two similar problems.  When they finished, they needed to check them on a calculator and find any errors.  There are so many problem types that work for this--and once students learn the process, there is no miscommunication on directions.
creative homework
 Another  favorite homework "type" for me is the "Make it Your Way" sheet...you can put ANYTHING in that oval and then ask them to generate a list of at least 10 (or 5 or 15 or whatever) ways to "make" that number or amount.  You will see students at a most basic of levels able to accomplish this...
homework ideas
 ...but also those who have additional skills can really showcase them.  This is where I'll see students playing with negative numbers, decomposing, and more--and the more they do, the more creative they get!  They just always have to be able to prove that they are right.  Again, once they are taught how to do it, there is no worry about directions.  These are GREAT for sharing the next day as well!  I often have students "star" their favorite 3 and then we do a gallery walk...or I let them write their favorite one on the Smartboard and we try to not get any repeats...lots of options.
creative homework
So...if I do assign homework, do I grade it?  Nope.  Students bring it into class in the morning and quickly buddy check it.  I check whether or not it was finished, and then partners work to reconcile any discrepancies!  End of story.  I am aware that there are people who are required to give and grade homework which just makes me a little sad...but perhaps you can come up with an easy rubric to use--related to effort, completion, and precision or something like that.

So anyway...I thought I'd just spark some discussion--either in the comments or in your own mine--about your own thoughts about homework for elementary students.  There certainly are MANY points of view--and many, many different situations.  I have actually changed my point of view over the last five years or so; I think it's always important to continually refine our beliefs and seek out deeper understanding.  Hope I got you thinking!

Want to see where I got these homework sheets?
Want to pin this post for later?   Here you go!

area and perimeter lessons
Some of my favorite math units/topics are those where I feel I have a handle on how to really get my students to construct their own understanding.  This is NOT the way most textbooks operate!  Most textbooks have you set a clear learning target:

I can find the perimeter of a rectangle by using the perimeter formula.

Then, the teacher models how to do the problems...talks through them...gives some guided practice...some independent practice--and then assesses student understanding.  It works--for some.

Instead, I really try to find ways to put students in situations where they are exploring, looking for patterns, and deriving their own rules.  I have found that this type of learning is more engaging, more meaningful, and "sticks" with the learner so much better.

Here's what this looked like with area and perimeter in my room last week.  Had I used our math series in sequence, the progression would have looked something like this:

1.  Teach the formula for the area of a rectangle.
2.  Teach finding the area of irregular shapes by decomposing into smaller rectangles.
3.  Teach the formula for the perimeter of a rectangle.
4.  Practice problems with area and perimeter.

I've been doing this fourth grade thing a long time--and I know my students aren't ready for that yet.  We still have a TON of misconceptions that need to be worked out before we move to formulas!  For example, many students still aren't crystal clear on the difference between perimeter and area--so I certainly don't want to teach formulas for concepts that they aren't confident about!

Also, students aren't ready to flexibly and correctly use labels (a "precision" issue!) related to units of length (ex. cm, in., m) as opposed to SQUARE units to measure area (we like to call it "squarea" to help with that!)

I also know from the past that students really struggle to even COUNT the squares on the side of a shape and often get confused between "inside" and "outside" of shapes.

There are other things that come up--there always are--but to jump right into formulas certainly doesn't give students time to explore, get these misconceptions corrected, and allow the time for them to build and deepen their own understanding.  Here are a few snippets of what I did BEFORE we tackled some of the work in our math book!

Our first investigation simply involved asking the students to build a rectangle using 12 tiles.  Students were able to do this with ease--and then I asked them to measure their rectangles, jot the answer on a sticky note, and come up to the group to share.

We had an amazing discussion about how to measure a rectangle!  Some measured only one way ("Mine was 6 squares long.") and others used two dimensions ("Mine was 3 one and 4 the other.").  I asked if anyone measured theirs and got 12.  No one had.  This led to a great chat about whether or not we should measure the INSIDE of a shape or the OUTSIDE--until we realized that BOTH could be valuable!  We came up with all sorts of real world examples when we would need to measure the outside edge or "rim" (peRIMeter) like fences, wallpaper borders, door frames, and so on. We also then talked about times when we might need to measure the entire area ("SQUAREA") in units that take up space...like for carpet or tile or planting sod and so on.  Once students were comfortable that there is more than one way to measure a rectangle, it was time to roll!
teaching area and perimeter
We continued building rectangles with set areas (like 12 square inches) and finding all sorts of different ways to do it--and we then compared the perimeters.  This was a great way for us to really stress the difference between measuring and counting the inches along the edge and the squares inside--two ways to "measure" rectangles.  Students started to notice what happened when they built long and skinny rectangles versus short "chubby" ones--and even were using correct vocabulary words like "length" and "width" and "perimeter".  We recorded our findings on a sheet and practiced using the correct labels--inches or square inches.

When it was clear that we were in pretty good shape in this department, I wanted to test their group work and problem solving!  This time, I told them they did NOT need to use rectangles--and that I wanted them to work in teams of 6 to solve a problem.  We talked about the problems that can arise with big groups (people being "bossy", people getting off-task, etc) so we set goals to stay focused and to strive for equal participation.  The task?  Have each person in the group create a shape with an area of 24 square inches--where no two people have the same perimeter!  This meant some people would have to give and take--and MAN it was interesting to watch some groups function (or NOT function as the case might be!)  
lesson plans area and perimeter
 It was so cool to listen to their discussions, the hints they gave each other, and the questions they asked.  Check out the shape one student came up with--which led to quite a debate within the group.  Can you do this?  Can there be a "void" (a student's word, not mine!) in the middle?  I listened to the debate for quite a while and then we agreed to solve it by agreeing that we would NOT count "voids"--and that all shapes had to be solid figures.  We called the other groups over to chime in--and then we reached consensus that we would proceed with that new rule.
teaching area and perimeter
As the groups solved the task and could prove that all 6 figures had different areas, they transferred their solution over to a grid page...
teaching area and perimeter
 Colored it...cut it...
teaching area and perimeter
I mounted them on black paper and hung them in the hall.  They have been receiving lots of attention from passers by!
area and perimeter lessons
The next day, I knew I wanted to continue to push their thinking before we dug into the formula, so I used this task--find three different rectangles that meet specific area and perimeter guidelines.  I reminded them that we have different tools in our classroom...tiles, graph paper, and so on--and sent them off to explore with their partners.
The discussions were amazing--and again, I reminded them to use the vocabulary list we had started on the board (I love to do this to keep that academic vocabulary fresh and accessible!) as they talked.  I circulated and asked questions, asked groups to show me their strategies, and so on.  Once they felt they had a solution, I told them to actually BUILD their rectangles!  Once they had their exact dimensions, it was time to replicate them with paper strips!
hands on math
It was amazing...as they worked, even MORE questions came up...some struggle with making right angles...some needed ruler help.  It was fascinating to watch--and I was able to do some "just in time" interventions.  The end product?  More "Area Art" to hang in the hall!
area and perimeter
By this point, I was feeling pretty confident that we understood the key differences between area nad perimeter and could find the area and perimeter of rectangles.  That lesson in our math series where I was supposed to TELL them the formulas?  Yeah...wasn't necessary.  They EASILY figured out the area and perimeter formulas as they worked through these investigations.  When I showed them the lesson, they laughed!  I heard things like, "Of course you multiply the length and width to get the area." and "There are lots of formulas to find the perimeter--not just the one in the book!".  We had fun making a list of all the formulas we could think of--and then evaluated which ones made the most sense to us!

There was a lesson in the book that was worth our time--finding the area of irregular shapes--but the students were SO comfortable with rectangles that they idea of "decomposing" these odd shapes was absolutely no big deal....but I want to talk more about that later because this post is already ridiculously long!  Thanks for sticking with me...I always just get so excited when I see learning make sense to my students--and that they can enjoy that learning process!

Want to see these activities and more?  Just click the image below.
Want to pin this post for later?  Here you go!
area and perimeter
Thanks for stopping by--and check back for "part two"!

standardized testing
Before we begin, I want to address the issue of standardized testing.  It is getting a pretty bad rap in the media and among teachers--and for good reason.  We test more than ever.  We spend more time PRACTICING to test than ever.  The stakes are higher than ever.  And this saddens me...because standardized testing DOES have a purpose when done in a reasonable way.  The simple truth is, we DO need a way to monitor our schools and our programs.  If my district finds that its elementary scores in fractions are dropping--we need to look at why.  If we notice trends in our special populations--we need to look at why.
teaching estimation lessons
So...as you may know, using math concept sorts is one of my absolute favorite strategies to get students thinking and talking about math.  I often used them sporadically in my units....sometimes as a "kick off" to see what they know...sometimes in the middle...sometimes as a review.

Today I thought I'd use one of my sorts that we didn't get to earlier as a great test prep review of multiplication and estimation.  I thought, "This will be an easy one...a good 25 minute warm up."

grade 3, grade 4, teaching line plots, line plot activities, hands on line plots, measurement activities, common core line plots, fraction line plots, analyzing line plots, making line plots, standardized testing
Chances are, if you teach third through fifth grades, the term "line plots" has become a part of your vocabulary.  If you give standardized tests, you've probably realized that test makers love them!  Unfortunately, many textbooks and other resources really don't seem to provide many rich and meaningful experiences with line plots.  Most activities are simple "create the plot" activities or are sets of questions that ask very basic information about the plots.  I wanted to find a way to make line plots more meaningful to my students, so I started by thinking of the following questions: